I've got a Chromecast and a Roku, what's the best way to watch live and recorded TV on either/both of these?

Roku is unsupported, but there is an alpha-quality channel posted in the Beta forum. The developers have stated that Roku as a platform for Channels is not part of their roadmap presently, so you're basically on your own there.

Chromecast is supported if you "cast from Chrome", quite literally. You can access the web UI and view which channel or recording you like, and then have Chrome (or another browser with casting support) cast the stream to your Chromecast device.

For inexpensive clients, your best option presently are Fire TV Stick 4Ks from Amazon. And, they are presently 50% off ($24.99 instead of $49.99) right now as part of their Black Friday sale.